Help with push email

That would be a setting in the email app. Usually where you can set the sync time - 15 minutes, 30 minutes, etc., there's a "Push" or "Automatic" setting. If there is none, the app you're using doesn't do push. About the best you can do to save battery with an app like that is to set it to Manual. When you open the app, it'll sync.
 
I use k9 mail as I can get push email for my @me.com account. Couldn't get push when on the nexus 4 so started using k9 and just carried on.

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All depends on your email provider, and if they support any of the push protocols like IMAP IDLE and so forth.

Of course gmail supports PUSH in the gmail app. For my other email accounts (IMAP IDLE), I use BlueMail. Wonderful email app. Look it up.